Hamiltonian torus actions on symplectic orbifolds and toric varieties

Eugene Lerman (MIT; presently Univ. of Illinois at Urban-Champaign); Susan Tolman (MIT)

Hamiltonian torus actions on symplectic orbifolds and toric varieties

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arxiv dg-ga/9511008 v1 pith:VFLCE6L7 submitted 1995-11-18 dg-ga math.DG

Eugene Lerman (MIT , presently Univ. of Illinois at Urban-Champaign) , Susan Tolman (MIT) This is my paper · ORCID

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keywords orbifoldsactionssymplectichamiltonianprovetorictorusvarieties

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In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half, we prove that compact symplectic orbifolds with completely integrable torus actions are classified by convex simple rational polytopes with a positive integer attached to each facet and that all such orbifolds are algebraic toric varieties.

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